OK, I think that in my rush to pontificate I somewhat misunderstood your original point. Which is actually quite embarassing, frankly. Sorry about that! Anyways, having re-read what you wrote I think I can see where you're coming from. I don't agree, but that's beside the point, and has more to do with my take on the red dwarf issue than with anything you wrote.

As a self-contained hypothesis, I think your reasoning is fairly sound. I'm not sure Pico island is the spot I would have chosen, as I'd be more inclined to think it would have been around the island of Bioko, right off of Camaroon, because the antipode is a lot closer to the center of the Pacific, plus I can see how the Camaroon rift (including the island chain) might have opened up if the planet was tidal locked with a red dwarf at the zenith there. However, the point is moot for me, since I don't think that's what happened. Still, all in all, you've got some interesting ramifications and I certainly can't "out proof you" with evidence towards what I believe, so I may well be wrong and you might be onto something. Keep it up!

Again Lynn Rose has made a case for there having been at least two such sub-dwarf-star points in past ages, neither one of which is Pico Island.

This one arose from nothing more complex than having new toys in the computer age, in this case Google Earth.

I never noticed the near total void of the Pacific in earlier years because all you ever had was globes which spun around on one axis. I was looking at the left coast and then trying to get a feel for WW-II geography and where Midway and the Mariannas were and I noticed the total void and I spun the thing around in a rough 180-degree arc and low and behold that mid Atlantic ridge and Pico Island. It was sort of stunning.